Carl tells his father that he has never struck one of his kids before he hit Julie but considering his anger, temper and fact he was ready to take a belt to his 17 year old daughter in the first episodes shows that this statement is most likely a lie.
Carl finds what he considers to be an inappropriate t-shirt for his daughter to be wearing but the t-shirt doesn't seem to fit with Julie's style of dress. She usually wears dresses or skirts with sweaters or blouses. She has not been shown wearing a t-shirt thus far in the show.